Pressure measurements, such as by pressure gauges that include a resonator made of piezoelectric crystal with the resonance frequency of the resonator changing as a result of the applied pressure, are affected by temperature. Similarly, with strain gauges, such as piezoresistive bridge gauges, including resistors with the resistances changing by deformation under pressure.
One example of a piezoelectric crystal pressure gauge, called Compensated Quartz Gauge (CQG), is described in U.S. Pat. No. 4,547,691. Due to specially selected crystal orientation, the aforementioned pressure gauge has dual-mode operation with two simultaneous bulk acoustic resonances; one is pressure dependent, Fc, at about 5.15 MHz and the other is temperature dependent, Fb, at about 5.60 MHz (at room temperature). Pressure and temperature readings can be computed from a polynomial equation of Fc, Fb and a set of coefficients implying that the pressure reading is calibrated with the temperature reading of the same pressure gauge. In contrast with CQG, other conventional pressure gauges operate in single-mode and use a thermometer installed adjacent to the pressure gauge to thermally calibrate pressure readings.
Conventional temperature calibration of CQG works well in the case of slow temperature variations. However, an adiabatic temperature variation, which happens due to a fast and large pressure variation, induces transient error in the pressure readings even in a dual-mode oscillation pressure gauge. A compensation algorithm for partial correction of the transient error is described in U.S. Pat. No. 5,394,345.
FIG. 1 shows a typical dynamic pressure response of the CQG against pressure drop from 5,000 psi to atmospheric pressure, and the pressure readings corrected with the foregoing conventional compensation algorithm. In FIG. 1, line 1-A indicates raw pressure readings and lines 1-B indicate corrected pressure readings. The corrected pressures, however, still show almost the same amplitude of overshoot error as the raw pressure readings.
Compared to a pressure gauge like the CQG that utilizes dual-mode oscillation to measure both pressure and temperature, single-mode oscillation pressure gauges have a disadvantage in terms of temperature compensation. In single-mode oscillation pressure gauges the gauge temperature is measured with a separate thermometer to compensate for temperature effects in pressure readings. The thermometer, however, cannot measure the gauge temperature correctly under transient temperature conditions because of a temperature gradient in the gauge packaging. This disadvantage is particularly emphasized in the case of adiabatic pressure changes. When pressure increases, the system temperature increases. When pressure decreases, the system temperature decreases. In a real situation, no perfect adiabatic condition exists, but is approximated when the time period of the pressure change is sufficiently shorter than the time period required for heat to flow in to or out from the system to attain thermal equilibrium.
Methods for calibration of single-mode oscillation pressure gauges have been proposed in, for example, U.S. Pat. No. 5,471,882. Since the conventional methods use a thermometer installed in the gauge packaging, and calculate a correction term by using temperature obtained from the thermometer, these methods are not suitable for correcting pressure measurements for errors due to rapid changes of temperature around the pressure gauge.
U.S. Pat. No. 4,607,530 describes compensation for single-mode oscillation pressure gauges using a thermometer outside the body of the pressure gauge, but the model adjustment parameters therein are estimated experimentally with a Kalman filter. Thus, a disadvantage is that the algorithm uses many model parameters that must be determined experimentally to correct the output frequency of the pressure gauge for ambient temperature variations.